Enter Relation and Dependencies
Example Data Table
| Relation | Functional Dependencies | Closure Request | Expected Closure | Candidate Key | Normal Form Note |
|---|---|---|---|---|---|
| R(A, B, C, D, E) | A → B,C; C → D; B,D → E | A⁺ | A, B, C, D, E | A | BCNF may fail when a determinant is not a superkey. |
| R(Student, Course, Teacher, Room) | Student,Course → Teacher; Teacher → Room | Teacher⁺ | Teacher, Room | Student, Course | Teacher → Room can create a transitive issue. |
| R(Order, Product, Price, Customer) | Order → Customer; Product → Price | Order, Product⁺ | Order, Product, Customer, Price | Order, Product | Partial dependencies can break second normal form. |
Formula Used
X⁺ = X plus every attribute Y where X functionally determines Y.
The closure algorithm starts with the selected attribute set X. It scans each dependency. If the left side is already inside the closure, the right side is added. The scan repeats until no new attribute appears.
X → Y holds when Y ⊆ X⁺.
Candidate keys are found by testing minimal attribute sets. A set is a superkey when its closure contains every relation attribute. It becomes a candidate key when no smaller subset is also a superkey.
BCNF rule: for every non-trivial X → Y, X must be a superkey.
The tool also checks 2NF and 3NF rules. Prime attributes come from candidate keys. Minimal cover is built by splitting right sides, removing extra left attributes, and deleting redundant dependencies.
How to Use This Calculator
- Enter all relation attributes in the first field.
- Type each functional dependency on a separate line.
- Enter the attribute set whose closure you want to find.
- Enter a left and right side to test a dependency.
- Press the calculate button.
- Review closure, keys, minimal cover, and normal form results.
- Use CSV or PDF buttons to save the report.
Functional Dependency Guide
Why Functional Dependencies Matter
Functional dependencies explain how data values control other data values. They are central to relational database design. A dependency such as Student ID → Student Name means one student ID gives one name. This rule helps designers remove duplication. It also helps them prevent update errors. A strong schema starts with clear dependency rules.
Understanding Attribute Closure
Attribute closure is the set of all attributes derived from a starting set. It answers a direct design question. What can this set determine? The calculator repeatedly applies each dependency. When the left side is available, the right side becomes available. The process stops when no more attributes can be added. Closure is useful for dependency testing. It is also useful for finding keys.
Candidate Keys and Minimal Covers
A candidate key is a minimal attribute set that determines the full relation. Minimal means no attribute can be removed. The calculator searches smaller sets first. It skips sets that contain an already found key. This makes the result easier to read. A minimal cover is another compact design tool. It rewrites dependencies into a simpler equivalent form. The process splits right sides. Then it removes unnecessary left side attributes. Finally, it deletes redundant dependencies.
Normal Form Analysis
Normal forms help reduce repeated facts. Second normal form checks partial dependency problems. Third normal form checks transitive dependency problems. Boyce-Codd normal form is stricter. It requires each determinant to be a superkey. The calculator highlights violations for each level. These warnings help you decide whether decomposition is needed. Use the output as a design guide. Then confirm business rules with real project requirements.
FAQs
1. What is a functional dependency?
A functional dependency means one attribute set determines another attribute set. For example, Employee ID can determine Employee Name.
2. What does attribute closure mean?
Attribute closure is every attribute that can be derived from a selected set using the given dependencies.
3. How does the calculator test X → Y?
It finds X closure first. If every Y attribute appears inside that closure, then X → Y holds.
4. What is a candidate key?
A candidate key is a minimal attribute set that determines all attributes in the relation.
5. What is a minimal cover?
A minimal cover is an equivalent dependency set with simpler left sides, single right sides, and no redundant rules.
6. What does BCNF mean?
BCNF means every non-trivial dependency must have a determinant that is a superkey.
7. Can I enter multiple right side attributes?
Yes. You can write A → B, C. The calculator splits them internally for minimal cover checks.
8. Is this suitable for database homework?
Yes. It shows closures, keys, covers, and normal form checks with readable steps for learning and review.